We follow the time dependent thermal evolution of a white dwarf ( WD ) undergoing sudden accretion in a dwarf nova outburst , using both simulations and analytic estimates .
The post-outburst lightcurve clearly separates into early times when the WD flux is high , and late times when the flux is near the quiescent level .
The break between these two regimes , occurring at a time of order the outburst duration , corresponds to a thermal diffusion wave reaching the base of the freshly accreted layer .
Our principal result is that long after the outburst , the fractional flux perturbation about the quiescent flux decays as a power law with time ( and not as an exponential ) .
We use this result to construct a simple fitting formula that yields estimates for both the quiescent flux and the accreted column , i.e .
the total accreted mass divided by WD surface area .
The WD mass is not well constrained by the late time lightcurve alone , but it can be inferred if the accreted mass is known from observations .
We compare our work with the well-studied outburst of WZ Sge , finding that the cooling is well described by our model , giving an effective temperature T _ { eff } = 14 , 500 { K } and accreted column \Delta y \approx 10 ^ { 6 } { g cm ^ { -2 } } , in agreement with the modeling of Godon et al .
To reconcile this accreted column with the accreted mass inferred from the bolometric accretion luminosity , a large WD mass \gtrsim 1.1 M _ { \odot } is needed .
Our power law result is a valuable tool for making quick estimates of the outburst properties .
We show that fitting the late time lightcurve with this formula yields a predicted column within 20 \% of that estimated from our full numerical calculations .